 Children enjoying some time reading at their desktops. |
The debate over computers in the schools has finally come around to giving naysayers equal time. There was an article in the Sunday New York Times regarding a school in the heart of California’s Silicon Valley that teaches math, music, and other standard elementary school subjects in a computer-free environment.Computers are touted as an enhancer for learning in education. However, data is unclear as to whether they do anything at all. There appear to do some things better, such as helping us to visualise certain concepts such as transformations in graphs in math. But it doesn’t help matters if by grade 10 a student is still lunging for his or her calculator to figure out 7×6. |
 A famous american president, reading at his desktop. |
The Waldorf school in the article appeared to have caught on to the idea that in order to learn something, your brain should be doing the work. A machine shouldn’t be doing the work for you. Otherwise, you are accepting your own obsolescence, and admitting to the world that you are replaceable by a machine.There is no substitute for a live, human teacher or the child’s own parent in helping a child learn. The Waldorf school bans computers up to at least grade 8, afterward allowing limited access to computer technology. Most user interfaces are braindead simple these days anyway. It takes you minutes to learn how to use your iTouch device. These days, if you have to read a manual to learn the operation of a new computer gizmo, the designers have failed. Windows and OSX are designed that way too. The learning of how to use a computer is easier than it has ever been, and students lose nothing by delaying their exposure to computers to a later age. |
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Well, that milestone had been past a couple of days ago having first been published on October 11, 1961 (I was sure it was first published in the 50s, but not so, according to publisher Simon & Schuster), but I must say it was my favourite book, and possibly remains my favourite book of fiction of all time. As is obvious by now, the book title originated the phrase, which is now often used to describe a no-win situation, or the state of being “between a rock and a hard place”. The book is uproariously funny, and I have read it twice over many years ago. I am not sure how it is that Joseph Heller found a way to make me laugh one minute and have me gasp over a major tragedy the next minute, but he found a way. There are not many books written like that, and as Stephen King said of Heller’s book: his style can’t be imitated. Whether it’s in favour of Euthanasia, or whatever other pretext there is to make suicide look good, do you ever notice that people in support of suicide are still alive, and need to be alive to advocate for it? I dunno. Just a thought. For my math class, I was attempting to create a curve sketching question by writing the second derivative as a factorable quadratic, and working backwards to an order-4 polynomial. Along the way, I would fill in the missing constant terms by using synthetic division on an arbitrary binomial factor, and striking upon a satisfactory polynomial by trial and error. What I was aiming for was for the original f(x) polynomial, its first derivative and its second derivative to all have rational roots. After about 6-8 hours of lackluster results (the only ones that worked by this method had triple roots), I tried the internet. It was then it became clear what an ambitious project this in fact was. I had downloaded graduate-level publications which try to tackle it. This has certainly helped me in generalizing the problem, but it appears to be something bordering on unwieldy given my time constraints. First of all, such polynomials which are differentiable and have rational roots in their first and second derivatives are called “Nice” polynomials. The impression I am getting is that these are fairly rare and difficult to find. Ones without double or triple roots have so far been next to impossible with my method, which I thought was airtight. Here was my plan: 1) I make a second derivative as a quadratic, which has rational factors. This gives me my points of inflection for when I obtain f(x). 2) Working backwards, the first derivative is found by the indefinite integral. The result will be a polynomial with an unknown constant term. That can be found by choosing an arbitrary binomial factor and synthetic division.
3) Working backwards once more, I found my quartic by finding f(x) through the indefinite integral of f ‘(x). I add the constant term once again by synthetic division using an arbitrary factor.
You might want to make a compromise and tell yourself that you’re willing to live with a situation that when using synthetic division, you wind up with quadratics that have real roots, but everything else works out OK. Then, your students have to use the quadratic formula, which isn’t necessarily a bad thing. It’s just that I don’t think such roots should occur too early. Getting them in f(x) is fine, but not really OK for its derivatives. I am a lover of satire, and I came across a great site called “Regretsy“, a parody site of “etsy“, which is a site for people who want to sell their arts and crafts. There are a lot of bad crafts out there sold by people who are often full of themselves (you have [...] Go to article Regretsy is into their second year. I recently purchased an OCZ Vertex 2 Solid State Hard Drive. The price per gig is enormous ($220 after taxes, in-store warranty, and mail-in rebate for a 120 gig hard drive), but is just the size to install the operating system and any applications I like. I generally don’t use the main hard drive [...] Go to article An SSD on an HP TX-2 Laptop with Linux It has come to my attention in recent years that we are the stupid ones. Homo sapiens, as we so arrogantly call ourselves, might be the least intelligent of the surviving genii of hominids. Our species won out over Homo neanderthalensis because we were more competitive and selfish than they. Neandethals have larger brains [...] Go to article Homage to species that barely existed Yesterday, I told another fellow computer geek an ’80s DOS joke about being prompted to “Enter any 11-digit prime number and press ENTER to continue.” She then suggested that a number with 11 1′s might be prime. Having encountered this before in programs I’ve written, I warned her that you can’t assume all sequences [...] Go to article How to spend an idle afternoon A couple of days ago at Harvard College was the first day that students had a chance to get settled away to their dorms; freshmen arrived with their parents, and clutches of parents and their young adult kids were clustered around the statue of John Harvard to have photos taken of them touching the [...] Go to article A Walk Around Harvard Yard I had been searching for a good USB keypad for use with my laptop. I prefer to enter sets of numbers using a separate keypad rather than using the “keypad mode” keys native to my laptop, since I don’t need to keep switching between modes if I am both entering a list of numbers [...] Go to article Keyboards and Keypads II 2:11 PM Tuesday 16 August I am sitting in the Catherine Stratton Lounge inside the Stratton Student Centre at MIT. At one end, a soap opera plays in a room where about 20 armchairs and couches are arranged on one end, theatre-style, around a 50-inch flat-screen TV. Only two students are lying there viewing [...] Go to article Cambridge Diary II 11:45 AM, Aug 15 I came out of the Boston subway system after taking the long way around to get to the Kendall/MIT stop. It’s raining, and I enter a building where I can get my first full meal, which is connected to a bookstore called the MIT co-op. There is a food court [...] Go to article Cambridge Diary I I have had a problem with dust, hair, and dirt accumulating on my keyboard, going in between and under keys thus and over time the keyboard gets increasingly difficult to use, even with compressed air. Elephant adds a silicone covering over the actual keyboard. The form-fitting layer is completely removable. Cleaning it is a [...] Go to article Keyboards and keypads I Rosanna, a 1982 single by a collection of former studio musicians called Toto would not be here due to the overall cheesiness of the video, but for a few overwhelming facts: The drum beat on the song, called a “half-time beat”, is a notoriously difficult one to play, but played gracefully by drummer Jeff [...] Go to article [Media Monday] Cheesy vintage video from Toto This photo shows my sound equipment used for generating voice recording on a laptop. The most prominent devices on the photo are the pair of Optimus microphones which have no hint of XLR connectivity, and just have quarter inch jacks. I bought them 10 years ago, and they have hardly been used. There is [...] Go to article [Media Monday] – Getting Sound equipment on the uber-cheap It is rather amazing that through all I have experienced, that these truths were the deepest and most enduring. They are also the most comforting. Simply keeping a balanced life, and looking on the positive side of things. What could possibly be wrong with that? Perhaps happiness and satisfaction with one’s life, however humble [...] Go to article So what if happiness is a mental illness? I keep saying how much of a fan I am of the RPN mode, and have used it on and off since high school. But times have changed, and HP needs to find a way to manipluate the logic of repeated calculations to make RPN still come out on top, but I feel discouraged, [...] Go to article HP 35s Calculator Annoyances III |
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